Abstract
Despite an increase in the number of experimental and numerical studies dedicated to spinal trauma, the influence of the rate of loading or displacement on lumbar spine injuries remains unclear. In the present work, we developed a bio-realistic finite element model (FEM) of the lumbar spine using a comprehensive geometrical representation of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The FEM was validated against published experimental data and used to compare the initiation sites of spinal injuries under low (LD) and high (HD) dynamic compression, flexion, extension, anterior shear, and posterior shear. Simulations resulted in force–displacement and moment-angular rotation curves well within experimental corridors, with the exception of LD flexion where angular stiffness was higher than experimental values. Such a discrepancy is attributed to the initial toe-region of the ligaments not being included in the material law used in the study. Spinal injuries were observed at different initiation sites under LD and HD loading conditions, except under shear loads. These findings suggest that the strain rate dependent behavior of spinal components plays a significant role in load-sharing and failure mechanisms of the spine under different loading conditions.
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References
Begeman PC, Visarius H, Nolte LP, Prasad P (1994) Viscoelastic shear response of the cadaver and Hybrid III lumbar spine. Presented at the 38th Stapp Car Crash Conference, Fort Lauderdale, FL, USA
Demotropoulos CK, Yang KH, Grimm MJ, Artham KK, King AI (1999) High rate mechanical properties of the Hybrid III and cadaveric lumbar spines in flexion and extension. In: 43rd Stapp Car Crash Conference Proceedings, San Diego, California
Demotropoulos CK, Yang KH, Grimm MJ, Khalil TB, King AI (1998) Mechanical properties of the cadaveric and Hybrid III lumbar spines. In: 42nd Stapp Car Crash Conference Proceedings, Tempe, Arizona
DiSilvestro MR, Suh JK (2001) A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression. J Biomech 34:519–525
Duma SM, Kemper AR, McNeely DM, Brolinson PG, Matsuoka F (2006) Biomechanical response of the lumbar spine in dynamic compression. Biomed Sci Instrum 42:476–481
El-Rich M, Arnoux PJ, Wagnac E, Brunet C, Aubin CE (2009) Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions. J Biomech 42:1252–1262
Fazzalari NL, Parkinson IH, Fogg QA, Sutton-Smith P (2006) Antero-postero differences in cortical thickness and cortical porosity of T12 to L5 vertebral bodies. Joint Bone Spine 73:293–297
Garo A, Arnoux PJ, Aubin CE (2009) Estimation of bone material properties using an inverse finite element method. Comput Methods Biomech Biomed Eng 12:121–122
Garo A, Arnoux PJ, Wagnac E, Aubin CE (2011) Calibration of the mechanical properties in a finite element model of a lumbar vertebra under dynamic compression up to failure. Med Biol Eng Comput 49:1371–1379
Groves CJ, Cassar-Pullicino VN, Tins BJ, Tyrrell PN, McCall IW (2005) Chance-type flexion-distraction injuries in the thoracolumbar spine: MR imaging characteristics. Radiology 236:601–608
Haug E, Choi HY, Robin S, Beaugonin M (2004) Human models for crash and impacts simulation. Special volume of Handbook of Numerical Analysis, XII. Elsevier B.V., North Holland
Hsu JM, Joseph T, Ellis AM (2003) Thoracolumbar fracture in blunt trauma patients: guidelines for diagnosis and imaging. Injury 34:426–433
Imai K, Ohnishi I, Bessho M, Nakamura K (2006) Nonlinear finite element model predicts vertebral bone strength and fracture site. Spine 31:1789–1794
Ivancic PC, Coe MP, Ndu AB, Tominaga Y, Carlson EJ, Rubin W et al (2007) Dynamic mechanical properties of intact human cervical spine ligaments. Spine J 7:659–665
Kazarian LE, Beers K, Hernandez J (1979) Spinal injuries in the F/FB-111 crew escape system. Aviat Space Environ Med 50:948–957
Kemper AR, McNally C, Duma SM (2007) The influence of strain rate on the compressive stiffness properties of human lumbar intervertebral discs. Biomed Sci Instrum 43:176–181
Kimura S, Steinbach GC, Watenpaugh DE, Hargens AR (2001) Lumbar spine disc height and curvature responses to an axial load generated by a compression device compatible with magnetic resonance imaging. Spine 26:2596–2600
King AI (2002) Injury to the thoracolumbar spine and pelvis. Accidental injury: biomechanics and prevention, 2nd edn. Springer, New York
Kosmopoulos V, Keller TS (2003) Finite element modeling of trabecular bone damage. Comput Methods Biomech Biomed Eng 6:209–216
Langrana NA, Harten RR, Lin DC, Reiter MF, Lee CK (2002) Acute thoracolumbar burst fractures: a new view of loading mechanisms. Spine 27:498–508
Leucht P, Fischer K, Muhr G, Mueller EJ (2009) Epidemiology of traumatic spine fractures. Injury 40:166–172
Magerl F, Aebi M, Gertzbein SD, Harms J, Nazarian S (1994) A comprehensive classification of thoracic and lumbar injuries. Eur Spine J 3:184–201
Neumann P, Nordwall A, Osvalder AL (1995) Traumatic instability of the lumbar spine. A dynamic in vitro study of flexion-distraction injury. Spine 20:1111–1121
Neumann P, Osvalder AL, Hansson TH, Nordwall A (1996) Flexion-distraction injury of the lumbar spine: influence of load, loading rate, and vertebral mineral content. J Spinal Disord 9:89–102
Ochia RS, Tencer AF, Ching RP (2003) Effect of loading rate on endplate and vertebral body strength in human lumbar vertebrae. J Biomech 36:1875–1881
Oloyede A, Broom ND (1993) A physical model for the time-dependent deformation of articular cartilage. Connect Tissue Res 29:251–261
Osvalder AL, Neumann P, Lovsund P, Nordwall A (1993) A method for studying the biomechanical load response of the (in vitro) lumbar spine under dynamic flexion-shear loads. J Biomech 26:1227–1236
Pintar FA, Yoganandan N, Myers T, Elhagediab A, Sances A Jr (1992) Biomechanical properties of human lumbar spine ligaments. J Biomech 25:1351–1356
Qiu TX, Tan KW, Lee VS, Teo EC (2006) Investigation of thoracolumbar T12–L1 burst fracture mechanism using finite element method. Med Eng Phys 28:656–664
Race A, Broom ND, Robertson P (2000) Effect of loading rate and hydration on the mechanical properties of the disc. Spine 25:662–669
Roberts S, McCall IW, Menage J, Haddaway MJ, Eisenstein SM (1997) Does the thickness of the vertebral subchondral bone reflect the composition of the intervertebral disc? Eur Spine J 6:385–389
Schmidt H, Heuer F, Simon U, Kettler A, Rohlmann A, Claes L et al (2006) Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus. Clin Biomech 21:337–344
Schmidt H, Kettler A, Heuer F, Simon U, Claes L, Wilke HJ (2007) Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading. Spine 32:748–755
Shirado O, Kaneda K, Tadano S, Ishikawa H, McAfee PC, Warden KE (1992) Influence of disc degeneration on mechanism of thoracolumbar burst fractures. Spine 17:286–292
Shirazi-Adl A (1994) Biomechanics of the lumbar spine in sagittal/lateral moments. Spine 19:2407–2414
Shirazi-Adl A, Ahmed AM, Shrivastava SC (1986) A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. J Biomech 19:331–350
Sundgren PC, Philipp M, Maly PV (2007) Spinal trauma. Neuroimaging Clin N Am 17:73–85
Tran NT, Watson NA, Tencer AF, Ching RP, Anderson PA (1995) Mechanism of the burst fracture in the thoracolumbar spine. The effect of loading rate. Spine 20:1984–1988
Wagnac E, Michardiere D, Garo A, Arnoux PJ, Mac-Thiong JM, Aubin CE (2010) Biomechanical analysis of pedicle screw placement: a feasibility study. Stud Health Technol Inform 158:167–171
Wagnac E, Aubin CE, El-Rich M, Arnoux PJ (2011) Finite element modeling of the lumbar spine ligaments for virtual trauma simulations. Med Eng Phys (MEP-D-11-00430)
Wagnac E, Aubin CE, Garo A, El-Rich M, Arnoux PJ (2011) Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads. J Biomech Eng 133:101007
White AA, Panjabi MM (1990) Clinical biomechanics of the spine, 2nd edn. J.B. Lippincott, Philadelphia
Wilcox RK, Allen DJ, Hall RM, Limb D, Barton DC, Dickson RA (2004) A dynamic investigation of the burst fracture process using a combined experimental and finite element approach. Eur Spine J 13:481–488
Yang KH, Hu J, White NA, King AI, Chou CC, Prasad P (2006) Development of numerical models for injury biomechanics research: a review of 50 years of publications in the Stapp Car Crash Conference. Stapp Car Crash J 50:429–490
Yingling VR, Callaghan JP, McGill SM (1997) Dynamic loading affects the mechanical properties and failure site of porcine spines. Clin Biomech 12:301–305
Yingling VR, McGill SM (1999) Anterior shear of spinal motion segments. Kinematics, kinetics, and resultant injuries observed in a porcine model. Spine 24:1882–1889
Zhao FD, Pollintine P, Hole BD, Adams MA, Dolan P (2009) Vertebral fractures usually affect the cranial endplate because it is thinner and supported by less-dense trabecular bone. Bone 44:372–379
Acknowledgments
This work was funded by research grants from the Natural Sciences and Engineering Research Council of Canada, the “Fonds de Recherche sur la Nature et les Technologies”, the “Ministère des Transports” of the Government of Quebec, and the “Commission Permanente de Coopération Franco-Québécoise”.
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There is no conflict of interest. Authors have not received any payment from industry for conducting this work and are in no conflict of interest.
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Wagnac, E., Arnoux, PJ., Garo, A. et al. Finite element analysis of the influence of loading rate on a model of the full lumbar spine under dynamic loading conditions. Med Biol Eng Comput 50, 903–915 (2012). https://doi.org/10.1007/s11517-012-0908-6
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DOI: https://doi.org/10.1007/s11517-012-0908-6